Magnetic Field & Forces
Visualize magnetic fields around wires and solenoids. See how charged particles curve in magnetic fields.
Key Notes
A moving charge creates a magnetic field and experiences a force in an external magnetic field.
The Lorentz force on a charge: F = qv × B. The force is always perpendicular to both v and B.
Since the force is perpendicular to velocity, the magnetic force does NO work on the charge (speed stays constant).
A charged particle in a uniform magnetic field moves in a circle if v ⊥ B, or a helix if v has a component along B.
Radius of circular motion: r = mv/(qB). Period: T = 2πm/(qB) — independent of velocity!
The cyclotron uses this principle: T is constant, so particles can be accelerated with a fixed-frequency oscillating field.
Biot-Savart Law: dB = (μ₀/4π)(Idl × r̂)/r² gives the magnetic field due to a current element.
Ampere's Circuital Law: ∮B·dl = μ₀I_enclosed — useful for high-symmetry situations.
Formulas
Lorentz Force
Force on moving charge in magnetic field.
Cyclotron Radius
Radius of circular orbit in B field.
Cyclotron Period
Independent of speed — key cyclotron principle.
Force on Current Wire
Force on a straight current-carrying conductor.
Biot-Savart Law
Field due to a current element.
Field of Long Wire
Magnetic field at distance r from infinite wire.
Important Points
Magnetic force cannot change speed, only direction — kinetic energy stays constant in a pure magnetic field.
The period T = 2πm/(qB) is independent of velocity — this is why the cyclotron works.
For a helical path, the pitch = v_parallel × T = (v cos θ)(2πm/qB).
Right-hand rule: curl fingers from v to B; thumb gives force direction for positive charge. Reverse for negative.
Two parallel currents in same direction attract; opposite directions repel. This defines the Ampere.
In JEE, magnetic field problems often combine with electric fields (velocity selector: qE = qvB, so v = E/B).
Magnetic Field & Forces notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.